javascript - Lazy Cartesian product of arrays (arbitrary nested loops)

Question

There are other questions about this in other languages, and other non-lazy JavaScript versions, but no lazy JavaScript versions that I have found.

Given an array of an arbitrary number of arbitrary-sized arrays:

var sets = [ [2,3,4,5], ['sweet','ugly'], ['cats','dogs','hogs'] ];

and a callback function:

function holla( n, adj, noun ){
  console.log( [n,adj,noun].join(' ') );
}

what's an elegant way to iterate the entire product space without creating a huge array of all possible combinations first?

lazyProduct( sets, holla );
// 2 sweet cats
// 2 sweet dogs
// 2 sweet hogs
// 2 ugly cats
// 2 ugly dogs
// 2 ugly hogs
// 3 sweet cats
// 3 sweet dogs
// 3 sweet hogs
// 3 ugly cats
// 3 ugly dogs
// 3 ugly hogs
// 4 sweet cats
// 4 sweet dogs
// 4 sweet hogs
// 4 ugly cats
// 4 ugly dogs
// 4 ugly hogs
// 5 sweet cats
// 5 sweet dogs
// 5 sweet hogs
// 5 ugly cats
// 5 ugly dogs
// 5 ugly hogs

---

Note that these combinations are the same as the results you would get if you had nested loops:

var counts     = [2,3,4,5];
var adjectives = ['sweet','ugly'];
var animals    = ['cats','dogs','hogs'];
for (var i=0;i<counts.length;++i){
  for (var j=0;j<adjectives.length;++j){
    for (var k=0;k<animals.length;++k){
      console.log( [ counts[i], adjectives[j], animals[k] ].join(' ') );
    }
  }
}

The benefits of the Cartesian product are:

1. It lets you nest an arbitrary number of loops (perhaps you don't know how many items you'll iterate)
2. It lets you change the order of looping (e.g. loop by adjectives first) without having to edit your code or write out all possible combinations of looping order.

---

Benchmarks

You can see the benchmarks for the answers below here:
http://jsperf.com/lazy-cartesian-product/26

Answer 1

A combination of recursion and iteration will do the job.

function lazyProduct(sets, holla) {
    var setLength = sets.length;
    function helper(array_current, set_index) {
        if (++set_index >= setLength) {
            holla.apply(null, array_current);
        } else {
            var array_next = sets[set_index];
            for (var i=0; i<array_next.length; i++) {
                helper(array_current.concat(array_next[i]), set_index);
            }
        }
    }
    helper([], -1);
}

Demo: http://jsfiddle.net/nV2XU/

var sets = [ [2,3,4,5], ['sweet','ugly'], ['cats','dogs','hogs'] ];
function holla( n, adj, noun ){
  console.log( [n,adj,noun].join(' ') );
}

lazyProduct(sets,holla);